arXiv Open Access 2026

Irrational series II Summation by packages

Olivier Thom
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Abstrak

Discrete sums of exponentials $g(w) = \sum a_β \mathrm{e}^{βw}$ with positive exponents may converge not normally in neighborhoods $H$ of $-\infty$ which do not contain half-planes. We study different notions of convergence for these series and in particular the intuitive notion of summation by packages. Indeed, joining in packages the terms in the sum $g(w)$ whose exponents are close together, and summing first inside each package may result in massive cancellations. We show that discrete sums $g(w)$ which are bounded in what we call logarithmic neighborhoods can always be summated by packages.

Topik & Kata Kunci

Penulis (1)

O

Olivier Thom

Format Sitasi

Thom, O. (2026). Irrational series II Summation by packages. https://arxiv.org/abs/2603.07350

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2026
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓